论文标题

HoneyTop90:使用HoneyComb Tessellation进行拓扑优化的90行MATLAB代码

HoneyTop90: A 90-line MATLAB code for topology optimization using honeycomb tessellation

论文作者

Kumar, Prabhat

论文摘要

本文提供了一种简单,紧凑,高效的90线教学MATLAB代码,用于使用六角元素(Honeycomb Tessellation)进行拓扑优化。六边形元素在两个并列元素之间提供了非分支连接性,因此,从优化的设计固有地构成了棋盘格的模式和点连接。提出了一种新型的生成蜂窝状缝线的方法。元素连接矩阵和相应的节点坐标阵列分别在5(7)和4(6)行中确定。在垂直方向上需要偶数元素的偶数元素需要两条额外的线。该代码需要一秒钟的时间来生成数百万六角形元素的网格格里德信息。 Wachspress形状函数用于有限元分析,并使用最佳标准方法进行合规性最小化。提供的MATLAB代码及其扩展名详细说明。提供有或没有过滤技术的优化的选项。还讨论了包括不同的边界条件,多个负载案例,主动和被动区域以及重型预测过滤器的步骤。该代码在附录〜a中提供,也可以从\ url {https://github.com/prabhatin/honeytop90}中下载它。

This paper provides a simple, compact and efficient 90-line pedagogical MATLAB code for topology optimization using hexagonal elements (honeycomb tessellation). Hexagonal elements provide nonsingular connectivity between two juxtaposed elements and, thus, subdue checkerboard patterns and point connections inherently from the optimized designs. A novel approach to generate honeycomb tessellation is proposed. The element connectivity matrix and corresponding nodal coordinates array are determined in 5 (7) and 4 (6) lines, respectively. Two additional lines for the meshgrid generation are required for an even number of elements in the vertical direction. The code takes a fraction of a second to generate meshgrid information for the millions of hexagonal elements. Wachspress shape functions are employed for the finite element analysis, and compliance minimization is performed using the optimality criteria method. The provided Matlab code and its extensions are explained in detail. Options to run the optimization with and without filtering techniques are provided. Steps to include different boundary conditions, multiple load cases, active and passive regions, and a Heaviside projection filter are also discussed. The code is provided in Appendix~A, and it can also be downloaded along with supplementary materials from \url{https://github.com/PrabhatIn/HoneyTop90}.

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